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Accounting & finance · Formula reference

Accounting and finance formulas, on one page

Nine formula cards with fictional worked examples: gross margin, profit margin and net income, cost of goods sold, contribution margin and break-even, straight-line and double-declining-balance depreciation, inventory turnover, current ratio, quick ratio and working capital, ROI, present and future value, and NPV. Then 20 practice questions with explanations and a summary that tells you which cards to reread. Free, no sign-up needed.

  • 9 formula cards
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  • 20 practice questions
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1 · Study cards

The formulas, with worked examples

Nine cards, each with the formula in plain words and fictional worked examples. Every example is worked out step by step. Jump to the card you need:

Study card 1

Gross profit, gross margin, net income and profit margin

A business starts with sales, subtracts what the goods cost it, then subtracts everything else. What is left after the cost of goods is gross profit; what is left after every expense is net income. A margin is one of those profits divided by sales, written as a percent.

The formulas

  1. Gross profit

    Net sales − cost of goods sold (COGS).

    Example: Sales of $80,000 with COGS of $48,000 leave $32,000.

  2. Gross margin (gross profit margin)

    Gross profit ÷ net sales × 100. The share of each sales dollar left after the cost of the goods.

    Example: $32,000 ÷ $80,000 = 0.40, so 40%.

    Note: Some sources use "gross margin" for the dollar amount. Check which your course means.

  3. Net income

    Revenues − all expenses: COGS, operating expenses, interest expense and income tax expense.

    Example: Sales $200,000 − COGS $120,000 − operating expenses $50,000 − interest $5,000 − taxes $6,000 = $19,000.

  4. Net profit margin (profit margin)

    Net income ÷ net sales × 100. When a question says only "profit margin," it usually means this one.

    Example: $19,000 ÷ $200,000 = 0.095, so 9.5%.

Worked examples

  1. Maple Street Bakery had sales of $80,000 and COGS of $48,000. Find gross profit and gross margin.

    1. Gross profit = 80,000 − 48,000 = 32,000.
    2. Gross margin = 32,000 ÷ 80,000 = 0.40.

    Answer: Gross profit $32,000; gross margin 40%

  2. Harbor Print Shop: sales $200,000, COGS $120,000, operating expenses $50,000, interest expense $5,000, income tax expense $6,000. Find net income and net profit margin.

    1. 200,000 − 120,000 = 80,000 gross profit.
    2. 80,000 − 50,000 − 5,000 − 6,000 = 19,000 net income.
    3. Net profit margin = 19,000 ÷ 200,000 = 0.095.

    Answer: Net income $19,000; net profit margin 9.5%

  3. A shop earned $18,000 gross profit at a 30% gross margin. What were its sales?

    1. Margin = gross profit ÷ sales, so sales = gross profit ÷ margin.
    2. 18,000 ÷ 0.30 = 60,000.

    Answer: Sales of $60,000

Watch out: Divide by sales, not by cost. A gross margin of 40% is not the same as a markup of 40%: markup divides the profit by the cost.

Study card 2

Cost of goods sold (COGS)

COGS is the cost of the goods a business actually sold in the period. It starts from what was on the shelf, adds what was bought, and takes away what is still on the shelf at the end.

The formulas

  1. Cost of goods available for sale

    Beginning inventory + purchases (net of returns and discounts, plus freight in).

    Example: $15,000 + $62,000 = $77,000.

  2. Cost of goods sold

    Beginning inventory + purchases − ending inventory.

    Example: $77,000 − $17,000 = $60,000.

  3. Ending inventory

    The cost of goods still unsold at the end of the period. It is a current asset, and it becomes next period’s beginning inventory.

    Example: COGS rearranged: ending inventory = goods available for sale − COGS.

Worked examples

  1. Lakeview Hardware began the year with $15,000 of inventory, bought $62,000 more and ended with $17,000. Find COGS.

    1. Goods available for sale = 15,000 + 62,000 = 77,000.
    2. COGS = 77,000 − 17,000 = 60,000.

    Answer: COGS $60,000

  2. Goods available for sale were $90,000 and COGS was $70,000. What was ending inventory?

    1. COGS = available − ending inventory, so ending inventory = available − COGS.
    2. 90,000 − 70,000 = 20,000.

    Answer: Ending inventory $20,000

  3. Using COGS of $60,000 and sales of $96,000, find the gross margin.

    1. Gross profit = 96,000 − 60,000 = 36,000.
    2. Gross margin = 36,000 ÷ 96,000 = 0.375.

    Answer: 37.5%

Watch out: Ending inventory is subtracted, not added: goods that are still unsold have not become an expense yet.

Study card 3

Contribution margin and break-even

Costs that change with how many units are made (materials, packaging) are variable. Costs that stay the same in total (rent, a salaried supervisor) are fixed. What each unit contributes toward the fixed costs, after its own variable cost, is the contribution margin. Break-even is the volume where the contributions exactly cover the fixed costs.

The formulas

  1. Contribution margin per unit

    Selling price per unit − variable cost per unit.

    Example: $25 − $10 = $15 per unit.

  2. Total contribution margin

    Sales − total variable costs.

    Example: $50,000 − $32,000 = $18,000.

  3. Contribution margin ratio

    Contribution margin ÷ sales (or per-unit margin ÷ price). Shown as a percent.

    Example: $15 ÷ $25 = 0.60, so 60%.

  4. Break-even point in units

    Fixed costs ÷ contribution margin per unit.

    Example: $4,500 ÷ $15 = 300 units.

  5. Break-even point in sales dollars

    Fixed costs ÷ contribution margin ratio.

    Example: $4,500 ÷ 0.60 = $7,500.

  6. Units for a target operating income

    (Fixed costs + target operating income) ÷ contribution margin per unit.

    Example: ($4,500 + $3,000) ÷ $15 = 500 units.

Worked examples

  1. A candle maker sells each candle for $25 with $10 of variable cost. Fixed costs are $4,500 a month. Find the break-even point in units and in sales dollars.

    1. Contribution margin per unit = 25 − 10 = 15.
    2. Break-even units = 4,500 ÷ 15 = 300.
    3. Check in dollars: 300 × 25 = 7,500, which equals 4,500 ÷ 0.60.

    Answer: 300 units, or $7,500 in sales

  2. Same candle maker. How many candles must be sold to earn an operating income of $3,000?

    1. Fixed costs plus the target: 4,500 + 3,000 = 7,500.
    2. Divide by the margin per unit: 7,500 ÷ 15 = 500.

    Answer: 500 candles

  3. A cafe had sales of $50,000 and total variable costs of $32,000. Find the contribution margin and its ratio.

    1. Contribution margin = 50,000 − 32,000 = 18,000.
    2. Ratio = 18,000 ÷ 50,000 = 0.36.

    Answer: $18,000; 36%

Watch out: Use the variable cost only. Gross margin subtracts all the cost of goods; contribution margin subtracts only the costs that change with volume.

Study card 4

Depreciation: straight-line and double-declining-balance

Depreciation spreads the cost of a long-lived asset over the years it is used. Straight-line spends the same amount every year. Double-declining-balance spends more early and less later.

The formulas

  1. Depreciable cost

    Cost − salvage value (what the asset is expected to be worth at the end of its useful life).

    Example: $30,000 − $3,000 = $27,000.

  2. Straight-line depreciation per year

    (Cost − salvage value) ÷ useful life in years.

    Example: $27,000 ÷ 5 = $5,400 a year.

  3. Double-declining-balance rate

    2 × (1 ÷ useful life). A 5-year life gives 2 × 20% = 40%.

    Example: 10-year life: 2 × 10% = 20%.

  4. Double-declining-balance expense

    Rate × beginning book value (cost − accumulated depreciation). Salvage value is ignored in the multiplication, but the asset is never depreciated below it.

    Example: Year 1 on a $20,000 asset at 40%: $8,000.

  5. Book value

    Cost − accumulated depreciation.

    Example: $20,000 − $8,000 = $12,000 after year 1.

Worked examples

  1. Equipment costs $30,000, has a salvage value of $3,000 and a 5-year life. Find the straight-line depreciation per year.

    1. Depreciable cost = 30,000 − 3,000 = 27,000.
    2. 27,000 ÷ 5 = 5,400.

    Answer: $5,400 a year

  2. A van costs $20,000, has a salvage value of $2,000 and a 5-year life. Find each year of double-declining-balance depreciation.

    1. Rate = 2 × 20% = 40%.
    2. Year 1: 40% × 20,000 = 8,000 (book value 12,000). Year 2: 40% × 12,000 = 4,800 (book value 7,200).
    3. Year 3: 40% × 7,200 = 2,880 (4,320). Year 4: 40% × 4,320 = 1,728 (2,592).
    4. Year 5 would be 1,036.80, which would drop book value below the 2,000 salvage value, so it stops at 592 (2,592 − 2,000).

    Answer: $8,000; $4,800; $2,880; $1,728; $592 (total $18,000)

Watch out: In double-declining-balance, do not subtract salvage value before multiplying, but stop when book value reaches salvage value.

Study card 5

Inventory turnover

Inventory turnover says how many times a business sold through and replaced its average stock of goods during the period. Higher turnover means goods move faster; what counts as a good number depends on the kind of business.

The formulas

  1. Average inventory

    (Beginning inventory + ending inventory) ÷ 2.

    Example: ($38,000 + $42,000) ÷ 2 = $40,000.

  2. Inventory turnover

    Cost of goods sold ÷ average inventory. The answer is a number of times, not a percent.

    Example: $240,000 ÷ $40,000 = 6 times.

Worked examples

  1. A garden store had COGS of $240,000, beginning inventory of $38,000 and ending inventory of $42,000. Find the inventory turnover.

    1. Average inventory = (38,000 + 42,000) ÷ 2 = 40,000.
    2. Turnover = 240,000 ÷ 40,000 = 6.

    Answer: 6 times

  2. A shop had COGS of $96,000 and an inventory turnover of 8. What was its average inventory?

    1. Turnover = COGS ÷ average inventory, so average inventory = COGS ÷ turnover.
    2. 96,000 ÷ 8 = 12,000.

    Answer: $12,000

Watch out: Use cost of goods sold on top, not sales. Inventory is recorded at cost, so the top must be at cost as well.

Study card 6

Working capital, current ratio and quick ratio

These three measures compare what a business has that will turn into cash within a year (current assets) with what it owes within a year (current liabilities).

The formulas

  1. Working capital

    Current assets − current liabilities. A dollar amount.

    Example: $70,000 − $40,000 = $30,000.

  2. Current ratio

    Current assets ÷ current liabilities. A ratio, often written 1.75 or 1.75 : 1.

    Example: $70,000 ÷ $40,000 = 1.75.

  3. Quick ratio (acid-test ratio)

    (Cash + short-term investments + net accounts receivable) ÷ current liabilities. It leaves out inventory and prepaid expenses.

    Example: ($12,000 + $8,000 + $20,000) ÷ $40,000 = 1.0.

    Note: Some textbooks write it as (current assets − inventory − prepaid expenses) ÷ current liabilities. Use the form your course teaches.

Worked examples

  1. Pine Ridge Supply has cash $12,000, short-term investments $8,000, net accounts receivable $20,000, inventory $25,000 and prepaid expenses $5,000. Current liabilities are $40,000. Find working capital, the current ratio and the quick ratio.

    1. Current assets = 12,000 + 8,000 + 20,000 + 25,000 + 5,000 = 70,000.
    2. Working capital = 70,000 − 40,000 = 30,000. Current ratio = 70,000 ÷ 40,000 = 1.75.
    3. Quick assets = 12,000 + 8,000 + 20,000 = 40,000. Quick ratio = 40,000 ÷ 40,000 = 1.0.

    Answer: Working capital $30,000; current ratio 1.75; quick ratio 1.0

  2. A business has a current ratio of 2.5 and current liabilities of $36,000. What are its current assets?

    1. Current ratio = current assets ÷ current liabilities, so current assets = ratio × current liabilities.
    2. 2.5 × 36,000 = 90,000.

    Answer: $90,000

Watch out: The quick ratio is never larger than the current ratio, because it takes assets out of the top. Negative working capital means current liabilities are larger than current assets.

Study card 7

Return on investment (ROI)

ROI compares what a project or division earned with what was put into it. Finance courses usually measure the net gain against the cost; managerial accounting courses often divide operating income by average operating assets. Both are a gain divided by an amount invested.

The formulas

  1. ROI (finance form)

    (Final value − cost) ÷ cost × 100, which is net gain ÷ cost.

    Example: A $40,000 project that returns $46,000: 6,000 ÷ 40,000 = 15%.

  2. ROI (managerial accounting form)

    Operating income ÷ average operating assets × 100.

    Example: $72,000 ÷ $600,000 = 12%.

    Note: Check which form your course uses; the examples here say which one they apply.

  3. Negative ROI

    The final value is below the cost, so the net gain is negative.

    Example: $5,000 that ends as $4,000: −1,000 ÷ 5,000 = −20%.

Worked examples

  1. A bakery spends $40,000 on a new oven line that brings back $46,000 in total. Find the ROI.

    1. Net gain = 46,000 − 40,000 = 6,000.
    2. ROI = 6,000 ÷ 40,000 = 0.15.

    Answer: 15%

  2. A division earned operating income of $72,000 on average operating assets of $600,000. Find its ROI (managerial form).

    1. ROI = 72,000 ÷ 600,000 = 0.12.

    Answer: 12%

  3. A purchase of $5,000 ended up worth $4,000. Find the ROI.

    1. Net gain = 4,000 − 5,000 = −1,000.
    2. ROI = −1,000 ÷ 5,000 = −0.20.

    Answer: −20%

Watch out: ROI ignores time. A 15% return that took one year and a 15% return that took five years show the same ROI.

Study card 8

Present value and future value

A dollar today and a dollar next year are not worth the same, because money can earn interest. Future value says what an amount today grows to. Present value goes the other way: what an amount due later is worth today.

The formulas

  1. Future value (FV)

    FV = PV × (1 + r)ⁿ, where r is the rate per period and n is the number of periods.

    Example: $2,000 at 5% for 2 years: 2,000 × 1.05² = $2,205.

  2. Present value (PV)

    PV = FV ÷ (1 + r)ⁿ. Discounting is compounding run backward.

    Example: $1,210 due in 2 years at 10%: 1,210 ÷ 1.10² = $1,000.

  3. Matching the rate and the period

    If interest is added twice a year, use half the yearly rate and twice the years.

    Example: 10% a year added semiannually for 1 year: 5% for 2 periods.

Worked examples

  1. Find the future value of $2,000 after 2 years at 5% a year, compounded yearly.

    1. (1.05)² = 1.1025.
    2. 2,000 × 1.1025 = 2,205.

    Answer: $2,205

  2. What is $1,210 due in 2 years worth today at 10% a year?

    1. (1.10)² = 1.21.
    2. 1,210 ÷ 1.21 = 1,000.

    Answer: $1,000

  3. Find the future value of $1,000 for 1 year at 10% a year, compounded twice a year.

    1. Rate per period = 10% ÷ 2 = 5%; periods = 2.
    2. 1,000 × 1.05² = 1,000 × 1.1025 = 1,102.50.

    Answer: $1,102.50

Watch out: The rate and the period must match: a yearly rate goes with years, a monthly rate with months. With a positive rate, more periods or a higher rate means a larger future value.

Study card 9

Net present value (NPV)

NPV puts every cash flow of a project in today’s dollars and adds them up. The money spent at the start is not discounted. Each later cash flow is discounted by the number of years until it arrives.

The formulas

  1. NPV

    NPV = (cash flow in year 1 ÷ (1 + r)) + (cash flow in year 2 ÷ (1 + r)²) + … − initial outlay.

    Example: Outlay $900, inflows $550 and $605, r = 10%: 500 + 500 − 900 = $100.

  2. Discount rate (r)

    The yearly rate used to bring future cash flows back to today.

    Example: 10% in the examples on this page.

  3. Reading the sign

    Positive NPV: the present value of the inflows is larger than the outlay. Negative: it is smaller. Zero: they are equal.

    Example: In a textbook decision rule, a positive NPV project is accepted.

Worked examples

  1. A project costs $900 now and returns $550 at the end of year 1 and $605 at the end of year 2. Find the NPV at a 10% discount rate.

    1. Year 1: 550 ÷ 1.10 = 500.
    2. Year 2: 605 ÷ 1.10² = 605 ÷ 1.21 = 500.
    3. NPV = 500 + 500 − 900 = 100.

    Answer: $100

  2. A project costs $1,100 now and returns $1,210 at the end of year 2. Find the NPV at 10%.

    1. Present value of the inflow = 1,210 ÷ 1.21 = 1,000.
    2. NPV = 1,000 − 1,100 = −100.

    Answer: −$100

Watch out: Discount each cash flow by its own year, and leave the initial outlay (time 0) as it is. The result depends on the discount rate chosen.

2 · Practice questions

20 practice questions

Twenty questions across the nine cards, in card order. Most are numbers to work out by hand and type (no calculator); a few are multiple choice. Each answer is explained at once, and the end is a summary by topic that says which cards to reread. Your result is free: no sign-up needed.

Question 1 of 20 · Gross margin, profit margin, net income

Sales are $50,000 and COGS is $30,000. What is gross profit?

Number in dollars (no need for $ or commas)

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Sources

Where the formulas come from

The formulas on this page follow these open textbooks from OpenStax, in our own words. Textbooks differ in small ways (the quick ratio and ROI especially), so the cards say which form they use. The businesses, names, numbers and worked examples are our own and invented. This is a study reference, not business, investment or tax advice; check anything important against your own course materials.

Rusty on the arithmetic behind the percents and ratios? Our free math refresher covers fractions, decimals and percents step by step. Heading back to school and not sure which program fits? The free skills finder turns what you have already done into a skills list.

Questions

Common questions

Gross margin = (net sales − cost of goods sold) ÷ net sales × 100. The top part, net sales minus COGS, is gross profit. A shop with $80,000 of sales and $48,000 of COGS has a gross profit of $32,000 and a gross margin of 32,000 ÷ 80,000 = 40%. Divide by sales, not by cost. Some sources use "gross margin" for the dollar amount, so check which one your course means.

Net profit margin = net income ÷ net sales × 100. Net income is what is left after every expense: cost of goods sold, operating expenses, interest and income tax. With net income of $19,000 on sales of $200,000, the margin is 9.5%. When a question says only "profit margin," it usually means this one, but gross, operating and net margins are all "profit margins" of a kind, so read the wording.

Current ratio = current assets ÷ current liabilities. With $70,000 of current assets and $40,000 of current liabilities the ratio is 1.75. Working capital uses the same two numbers but subtracts: $70,000 − $40,000 = $30,000. The quick ratio is stricter: it counts only cash, short-term investments and net accounts receivable, so inventory and prepaid expenses are left out.

Cost of goods sold = beginning inventory + purchases − ending inventory. Net income = revenues − all expenses. For example, $15,000 of beginning inventory plus $62,000 of purchases is $77,000 of goods available for sale; subtract $17,000 of ending inventory and COGS is $60,000. Subtract COGS, then every other expense, from sales to reach net income.

Break-even units = fixed costs ÷ contribution margin per unit, and contribution margin per unit = selling price − variable cost per unit. With a $25 price, $10 of variable cost and $4,500 of fixed costs, each unit contributes $15, so break-even is 300 units, or $7,500 of sales. In sales dollars, divide fixed costs by the contribution margin ratio instead.

Straight-line spends the same amount every year: (cost − salvage value) ÷ useful life. Double-declining-balance multiplies the beginning book value by twice the straight-line rate (40% for a 5-year life), so the expense is largest in year 1 and shrinks. It ignores salvage value in the multiplication, but the asset is never depreciated below its salvage value.

Future value is what an amount today grows to: FV = PV × (1 + r)ⁿ. Present value runs it backward: PV = FV ÷ (1 + r)ⁿ. Net present value adds up the present values of a project’s later cash flows and subtracts the initial outlay, so a positive NPV means the present value of the inflows is larger than the outlay. The rate and the number of periods must use the same time unit.

No. The cards are a formula reference with fictional worked examples, and the practice questions ask you to work a number out by hand and type it, or to choose an answer. It is a study aid for introductory accounting and finance courses, not business, investment or tax advice.

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